Summary

This fifth edition book bridges the gap between the theory and practice of derivatives. It provides a unifying approach to the valuation of all derivatives--not just futures and options. It assumes that the reader has some knowledge of finance and probability and statistics. Topics covered include Determination of Forward and Futures Prices, Interest Rate Markets, Mechanics of Options Markets, and Properties of Stock Options. For individuals who work for banks and other financial institutions, as well as options traders, options analysts, risk managers, swaps traders, financial engineers, and corporate treasurers.

Table of Contents

Preface

xix

Introduction

1

(18)

Exchange-traded markets

1

(1)

Over-the-counter markets

2

(1)

Forward contracts

2

(3)

Futures contracts

5

(1)

Options

6

(4)

Types of traders

10

(4)

Other derivatives

14

(5)

Summary

15

(1)

Questions and problems

16

(1)

Assignment questions

17

(2)

Mechanics of futures markets

19

(22)

Trading futures contracts

19

(1)

Specification of the futures contract

20

(3)

Convergence of futures price to spot price

23

(1)

Operation of margins

24

(3)

Newspaper quotes

27

(4)

Keynes and Hicks

31

(1)

Delivery

31

(1)

Types of traders

32

(1)

Regulation

33

(2)

Accounting and tax

35

(1)

Forward contracts vs. futures contracts

36

(5)

Summary

37

(1)

Suggestions for further reading

38

(1)

Questions and problems

38

(2)

Assignment questions

40

(1)

Determination of forward and futures prices

41

(29)

Investment assets vs. consumption assets

41

(1)

Short selling

41

(1)

Measuring interest rates

42

(2)

Assumptions and notation

44

(1)

Forward price for an investment asset

45

(2)

Known income

47

(2)

Known yield

49

(1)

Valuing forward contracts

49

(2)

Are forward prices and futures prices equal?

51

(1)

Stock index futures

52

(3)

Forward and futures contracts on currencies

55

(3)

Futures on commodities

58

(2)

Cost of carry

60

(1)

Delivery options

60

(1)

Futures prices and the expected future spot price

61

(9)

Summary

63

(1)

Suggestions for further reading

64

(1)

Questions and problems

65

(2)

Assignment questions

67

(1)

Appendix 3A: Proof that forward and futures prices are equal when interest rates are constant

68

(2)

Hedging strategies using futures

70

(23)

Basic principles

70

(2)

Arguments for and against hedging

72

(3)

Basis risk

75

(3)

Minimum variance hedge ratio

78

(4)

Stock index futures

82

(4)

Rolling the hedge forward

86

(7)

Summary

87

(1)

Suggestions for further reading

88

(1)

Questions and problems

88

(2)

Assignment questions

90

(2)

Appendix 4A: Proof of the minimum variance hedge ratio formula

92

(1)

Interest rate markets

93

(32)

Types of rates

93

(1)

Zero rates

94

(1)

Bond pricing

94

(2)

Determining zero rates

96

(2)

Forward rates

98

(2)

Forward rate agreements

100

(2)

Theories of the term structure

102

(1)

Day count conventions

102

(1)

Quotations

103

(1)

Treasury bond futures

104

(6)

Eurodollar futures

110

(1)

The LIBOR zero curve

111

(1)

Duration

112

(4)

Duration-based hedging strategies

116

(9)

Summary

118

(1)

Suggestions for further reading

119

(1)

Questions and problems

120

(3)

Assignment questions

123

(2)

Swaps

125

(26)

Mechanics of interest rate swaps

125

(6)

The comparative-advantage argument

131

(3)

Swap quotes and LIBOR zero rates

134

(2)

Valuation of interest rate swaps

136

(4)

Currency swaps

140

(3)

Valuation of currency swaps

143

(2)

Credit risk

145

(6)

Summary

146

(1)

Suggestions for further reading

147

(1)

Questions and problems

147

(2)

Assignment questions

149

(2)

Mechanics of options markets

151

(16)

Underlying assets

151

(1)

Specification of stock options

152

(3)

Newspaper quotes

155

(2)

Trading

157

(1)

Commissions

157

(1)

Margins

158

(2)

The options clearing corporation

160

(1)

Regulation

161

(1)

Taxation

161

(1)

Warrants, executive stock options, and convertibles

162

(1)

Over-the-counter markets

163

(4)

Summary

163

(1)

Suggestions for further reading

164

(1)

Questions and problems

164

(1)

Assignment questions

165

(2)

Properties of stock options

167

(18)

Factors affecting option prices

167

(3)

Assumptions and notation

170

(1)

Upper and lower bounds for option prices

171

(3)

Put-call parity

174

(1)

Early exercise: calls on a non-dividend-paying stock

175

(2)

Early exercise: puts on a non-dividend-paying stock

177

(1)

Effect of dividends

178

(1)

Empirical research

179

(6)

Summary

180

(1)

Suggestions for further reading

181

(1)

Questions and problems

182

(1)

Assignment questions

183

(2)

Trading strategies involving options

185

(15)

Strategies involving a single option and a stock

185

(2)

Spreads

187

(7)

Combinations

194

(3)

Other payoffs

197

(3)

Summary

197

(1)

Suggestions for further reading

198

(1)

Questions and problems

198

(1)

Assignment questions

199

(1)

Introduction to binomial trees

200

(16)

A one-step binomial model

200

(3)

Risk-neutral valuation

203

(2)

Two-step binomial trees

205

(3)

A put example

208

(1)

American options

209

(1)

Delta

210

(1)

Matching volatility with u and d

211

(1)

Binomial trees in practice

212

(4)

Summary

213

(1)

Suggestions for further reading

214

(1)

Questions and problems

214

(1)

Assignment questions

215

(1)

A model of the behavior of stock prices

216

(18)

The Markov property

216

(1)

Continuous-time stochastic processes

217

(5)

The process for stock prices

222

(1)

Review of the model

223

(2)

The parameters

225

(1)

Ito's lemma

226

(1)

The lognormal property

227

(7)

Summary

228

(1)

Suggestions for further reading

229

(1)

Questions and problems

229

(1)

Assignment questions

230

(2)

Appendix 11A: Derivation of Ito's lemma

232

(2)

The Black-Scholes model

234

(33)

Lognormal property of stock prices

234

(2)

The distribution of the rate of return

236

(1)

The expected return

237

(1)

Volatility

238

(3)

Concepts underlying the Black-Scholes-Merton differential equation

241

(1)

Derivation of the Black-Scholes-Merton differential equation

242

(2)

Risk-neutral valuation

244

(2)

Black-Scholes pricing formulas

246

(2)

Cumulative normal distribution function

248

(1)

Warrants issued by a company on its own stock

249

(1)

Implied volatilities

250

(1)

The causes of volatility

251

(1)

Dividends

252

(15)

Summary

256

(1)

Suggestions for further reading

257

(1)

Questions and problems

258

(3)

Assignment questions

261

(1)

Appendix 12A: Proof of Black-Scholes-Merton formula

262

(3)

Appendix 12B: Exact procedure for calculating the values of American calls on dividend-paying stocks